1. Field of the Invention
The present invention relates to a method and apparatus for automatically selecting Bragg reflections and to a method and system for automatically determining crystallographic orientation, which are useful in analyzing and characterizing structures of crystal samples such as wafers for semiconductor and thin films deposited on the wafers.
2. Description of the Related Art
In crystal structure analysis developed for analysis of atomic structure, x-rays, or particles beams such as neutron beams or electron beams are applied to a crystal sample with the unknown structure, and then, using diffraction phenomenon of rays scattered by the crystal sample, the lattice type of the crystal sample or the atomic arrangement in the lattice are clarified. In this crystal structure analysis, for example, x-rays are used for the analysis of electron density in the crystal sample, neutron beams are used for the analysis of atomic nuclei positions in the crystal sample, and electron beams are used for the analysis of electric potential in the crystal sample.
On the other hand, a method, so-called two-reflection method, for determining the crystallographic orientation of a crystal sample having known crystal structure has been utilized frequently. In this two-reflection method, two Bragg reflections in the recipricol space of the crystal sample are searched, and then the crystallographic orientation are determined using the positions of the obtained two Bragg reflections.
More specifically, in this two-reflection method, first, when the reciprocal lattice of a crystal sample is at the standard position, reference Bragg reflections K.sub.1 and K.sub.2 together forming a basis for determination of crystallographic orientation of this crystal sample are selected arbitrarily, as shown in FIG. 1(a). Next, actual Bragg reflections K.sub.1 ' and K.sub.2 ' satisfying their diffraction conditions, i.e., 2.theta.-angles, .omega.-angles, .chi.-angles, and .phi.-angles, of the reference Bragg reflections K.sub.1 and K.sub.2, respectively, are actually measured with a four-axis goniometer system, as shown in FIG. 1(b). Then, rotation angle from the reference position of the reciprocal lattice is determined using the positions of the actual Bragg reflections K.sub.1 ' and K.sub.2 ' (i.e., using the rotation angles from the reference Bragg reflections K.sub.1 and K.sub.2 to the actual Bragg reflections K.sub.1 ' and K.sub.2 '). In this way, the actual crystallographic orientation of the crystal sample are determined.
A four-axis goniometer system is well-known in the art. For example, as shown in FIGS. 2 and 3, the four-axis goniometer system comprises a 4-axis goniometer 100 having four rotating axes (i.e., an .OMEGA.-axis for determining the crystal direction of a crystal sample 200, a X-.PHI. assembly carried on the .OMEGA.-axis, and 2.theta.-axis for detecting diffracted x-rays), an x-ray source 110, a detector 120 such as an x-ray counter for detecting diffracted rays, a computer 130 used for control, and a 2.theta.-rotation driving device 141, an .OMEGA.-rotation driving device 142, a .chi.-rotation driving device 143 and a .phi.-rotation driving device 144 for rotating the respective rotation axes of the 4-axis goniometer 100. The computer 130 has a CPU 131, a memory 132, and a CRT display 133.
The rotation angles of the 2.theta.-axis, .OMEGA.-axis, X-axis, and the .phi.-axis of the 4-axis goniometer 100 are, respectively, 2.PHI.-angle that is the angle of diffraction, .omega.-angle that is the angle of incidence, .chi.-angle that is the tilt angle of the crystal sample 200, and .phi.-angle that is the angular position of the crystal sample 200 on the .PHI.-axis.
The computer 130 controls the 2.theta.-rotation driving device 141, the .omega.-rotation driving device 142, the .chi.-rotation driving device 143, and the .phi.-rotation driving device 144 so as to rotate the 2.theta.-axis, .OMEGA.-axis, X-axis, and .PHI.-axis so that the actual angles of the 4-axis goniometer 100 becomes equal to the diffraction conditions, i.e., 2.theta.-angles, .omega.-angles, .chi.-angles, and .phi.-angles, of the reference Bragg reflections K.sub.1 and K.sub.2. Then, the diffracted x-rays at these 2.theta.-angles, .omega.-angles, .chi.-angles, and .phi.-angles, i.e., the actual Bragg Reflections K.sub.1 ' and K.sub.2 ' satisfying the diffraction conditions, are detected by the detector 120.
However, in this prior art method for determining the crystallographic orientation using the two-reflection method described above, the two reference Bragg reflections K.sub.1 and K.sub.2 forming a basis for the determination of the crystallographic orientation must be selected manually. Automatic selection techniques using a computer are not yet established. Therefore, after selecting the reference Bragg reflections K.sub.1 and K.sub.2 manually, actual Bragg reflections K.sub.1 ' and K.sub.2 ' must be measured in additional experiments to find the positions accurately, and then the crystallographic orientation are computed. Thus, determination of the crystallographic orientation in one continuous process could not have been made, thereby making it very cumbersome to perform and time-consuming. Consequently, there has been a great demand for an technique capable of automatically determining the crystallographic orientation in one continuous process.